**COMPARISON BETWEEN PARALLELING LOADS CONNECTED TO ANTENNA OUTPUT OR SPLITTING WITH 3 db HYBRIDS**

In the previous thread on 3 dB Hybrid Couplers we have seen that one of the advantages of these devices is ISOLATON. It is isolation that avoids Local Oscillator interference among receivers fed from the same antenna. But another extremely important advantage is the fact that the use of 3 dB hybrid couplers allows power splitting with MINIMAL LOSS. By using the simple Ohm's law the numerical example below compares the power loss by using a 4 way 3 db Hybrid (loss that we have measured & demonstrated in the previous post to be 1 dB) to the power loss experienced by paralleling the input of the receivers with T's.

With a 3 dB/4 way Hybrid, starting with a power of 80 mW (2 V on 50 Ohm, as the value for the example) each receiver sees 63.49 mW, e.g. minimal loss. Paralleling the 4 receivers, each receiver sees only 3.2 mW and the insertion loss becomes 13 dB!

The reader, looking at calculations below, will ask the following question: where is the power gone with the parallel connection of 4 receivers?

Most of the power is dissipated across the 50 Ohm source impedance, because this load is no more 50 Ohm (as it is with the 3 dB Hybrid) but 12.5 Ohm, for reason of the parallel connection. So current out of antenna tends to increase and there is more voltage drop across its 50 Ohm source impedance. A second reason of the loss is the fact that each of the parallel receivers sees the voltage relative to 12.5 Ohm, BUT ITS IMPEDANCE IS 50 OHM, so the power in dBm is sees is lower in the ratio of the two impedances squared.

Please appreciate that this is a very optimistic calculation, valid only if the antenna is connected directly to the 4 paralleled receivers without coaxial cable, so the negative effect of REFLECTIONS is not taken into consideration. In a future post we shall define VSWR, explain its meaning and calculate what the difference in insertion loss would be.

Antenna system impedance Zo, Ohm 50 Ohm

Number of loads, n 4

Single load impedance, Zk, Ohm 50 Ohm

Antenna Voltage, Va, 2 V

Antenna nominal power Pa, Pa=(Va^2)/50 = 0.08 W

Antenna nominal power Pa1, 80 mW

3dB Hybrid loss, dB / ratio r1 1.26

Power in loads, Pl, Pl=Pa/r = 63.49 mW

Composite load impedance Zkc, Zkc=Zk/n = 12.5 Ohm

Antenna current Ia, Ia=Va*1000/(Zo+Zkc)= 32mA

Voltage across composite load Vc, Vc=Zkc*Ia/1000 = 0.4 V

Power delivered to composite loads Pll, Pll=(Vc^2)/Zkc = 12.8 mW

Effective power loss, ratio Lr Lr=Pa1/Pll = 6.25

Effective power loss Lrd 7.96 dB

Power seen by each load Pa2 Pa2=(Vc^2)*1000/Zk = 3.2 mW

Difference in power, ratio dk dk=Pl/Pa2 = 19.84126984

Difference in power dB, Dd

**12.97 dB**